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Nevertheless, it is correct to say that the likelihood function itself is not necessarily a probability density. For example, if the data for 2 tosses of a coin is (heads,heads), and the probability of heads is the variable p, then adding up the likelihoods for the values p = .9, p = .8 gives
172:"the "distribution" of an unobserved variable given data is rather the likelihood function (which is not a distribution)" - this is not correct, the likelihood function is if at all the distribution of the probability of obtaining the data as a function of a parameter.
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For a given set of data, the maximum likelihood estimate is the value of the parameter that is most likely, because it most closely approximates the data distribution if the parameter value was equal to the maximum likelihood estimate.
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The likelihood function is a function that gives the likelihood of a parameter given the data. A profile likelihood shows the likelihoods of different values on the parameter, given the data.
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Baldly saying "the "distribution" of data given the unobserved variable is rather the likelihood function (which is not a probability distribution)" is deeply confusing.
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If you sum it over different values of the parameter for a particular vector of data, that will not sum to one. But, contrariwise, if you sum it
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a probability distribution. If you want to say that the likelihood function is (generally) not a probability distribution
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What is meant by block difference inverse probability? anyone please let me know...thanks mail me anandhmurali@gmail.com
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Knowledge. If you would like to participate, please visit the project page, where you can join
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The point here surely is that the likelihood function is not a probability distribution
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a probability distribution for the data, given some value of the parameter.
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